Ab initio investigations of magnetic properties of ultrathin transition ...

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4.3 3d-Monolayers on Rh(111) Substrate: 69 moments on square lattices. Additionally, the RW-AFM structure is not the only possible anti-ferromagnetic spin configuration on hexagonal substrates due to spin frustrations on triangular lattices as we will see later. Therefore, Rh(I) atoms will always have induced moments in case of any collinear AFM arrangement on hexagonal surfaces, although the are considerably small compared to those where induced ferromagnetically. Table 4.2: Results of optimized interlayer distance (in ˚A), obtained from FM (AFM) relaxations, between 3d monolayer and Rh(I) of Rh(001) and Rh(111) substrates. V Cr Mn Fe Co Ni Rh(001) 1.77 (1.77) 1.69 (1.81) 1.77 (1.73) 1.77 (1.67) 1.66 (1.65) 1.67 (1.65) Rh(111) 2.07 (-) - (2.09) 2.16 (2.08) 2.07 (2.02) 2.01 (2.01) 2.03 (2.03) The largest induced magnetic moments are caused by the Co and Ni monolayers on both Rh surfaces. This is due to their strong ferromagnetism and strongest inward relaxations with smallest interlayer distance from Rh(I) as shown in table 4.2. The induced moments from the FM calculations are larger for Rh(001) than for Rh(111) substrate due to the difference in the coordination number, as well as smaller 3d-Rh(I) interlayer distance. For the RW-AFM results, the Rh(I) atoms have almost zero magnetic moments induced by Cr or Mn, where they are noticeable for Fe, Co and Ni because of their large inward relaxations on Rh(111) (see fig. 4.15(right)) 4.3.2 Magnetic order: Collinear calculations were performed to calculate the total energy difference ΔE = EAFM− EFM between the RW-AFM and the FM relaxed configurations. The results are plotted in Fig.4.17 for the 3d TM monolayers on Rh(111)substrate, and compared to Rh(001) substrate results. For the Rh(111) substrate, we found that FM solution is more stable for Fe, Co and Ni, while it is c(2 × 2) AFM for Mn. As mentioned above, Cr (V) has no stable FM (RW-AFM) solution on Rh(111), therefore we are unable to calculate total energy difference. Except for Fe, the results of Rh(111) substrate show no difference in the 3d magnetic order from what we obtained on the Rh(001) substrate. Using equation (3.11), a stronger tendency towards ferromagnetism is expected for large nonmagnetic LDOS at Fermi level, which means smaller band width (eq. 3.14) and then smaller coordination number (eq. 3.16), keeping the nearest neighbor distance constant. For different magnetic configurations of Fe on Rh substrate, we calculated the local density of states of the Fe monolayer on Rh(111) surface, and then compare the results to Fe density of states on Rh(001) as shown in figure 4.18. From the nonmagnetic calculations, we see that the Fe LDOS –at Fermi level– on Rh(001) is larger than Fe NM LDOS on Rh(111) substrate. These nonmagnetic results of LDOS agrees with the expectation that systems with large coordination number will have wider band width and then smaller nonmagnetic density of states, which is the case for Fe/Rh(111) NM LDOS. But according to the Stoner model, Fe/Rh(001) should be more FM than on Rh(111).
70 4 Collinear magnetism of 3d-monolayers on Rh substrates E [meV./3d-atom] Δ 400 300 200 100 0 −100 −200 −300 −400 FM AFM 1 ML 3d on Rh(001) Rh(111) Ag(001) Pd(001) Rh(001) W(001) Rh(001) V Cr Mn Fe Co Ni Figure 4.17: Total energy difference for different magnetic order of 3d TMs on Rh(111) (circles) and Rh(001) (squares) surfaces: positive ΔE = EAFM − EFM indicates that FM is more stable, while negative values denote AFM order. From the magnetic LDOS, we see that in the case of Fe/Rh(001) Fe has larger FM LDOS AFM, therefore the AFM configuration is more stable, while Fe FM is smaller than the AFM LDOS in the case for Fe/Rh(111) leading to more stability of FM solution. Finally, we should notice that we calculated Fe ground state on Rh(111) by total energy difference between FM and the RW-AFM configurations, but on hexagonal lattices, the magnetic spins are frustrated if they prefer to align anti-ferromagnetically. In our comparison between Fe/Rh(111) and Fe/Rh(001) we chosen the collinear RW-AFM spins arrangement on Rh(111) surface, which is not the only collinear solution to construct an anti-ferromagnetic structures on hexagonal substrates. There are many collinear and noncollinear spin structures where the spins might align non-ferromagnetically in two or three dimensions, simplest example is the famous 120 ◦ Néel magnetic structure on hexagonal lattice. This leads us to further investigations in next chapter to find the true magnetic ground state of Fe on Rh(111) and other hexagonal substrates. As a conclusion of this chapter, We employed the full-potential linearized augmented plane-wave method to report a systematic density-functional study of the magnetic properties of the 3d transition-metal (V, Cr, Mn, Fe, Co and Ni) monolayers deposited on the Rh(001) and Rh(111) substrates. Performing collinear calculations, we relaxed our structures using atomic force calculations, and compared the FM and AFM relaxations on both Rh surfaces. we found, all monolayer films are magnetic. The size of the local magnetic moments across the transition-metal series follows Hund’s rule with a maximum magnetic moment of 3.77 μB for Mn. The largest induced magnetic moment of about 0.46 μB was found for Rh atoms adjacent to the Co-film on Rh(001). When relaxations are included, we predict a ferromagnetic (FM) ground state for V, Co and Ni, while Cr,
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Mitglied der Helmholtz-Gemeinschaft
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Forschungszentrum Jülich GmbH Inst
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Abstract In this thesis, we investi
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”A human being is part of the who
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II Contents 4.2.1 Relaxations and m
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2 INTRODUCTION (ao =3.80 ˚A) is in
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4 INTRODUCTION understanding of our
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6 INTRODUCTION
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8 1 Density functional theory (DFT)
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10 1 Density functional theory (DFT
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16 2 The FLAPW method 1 0 0 1 Figur
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120 where, the relation � i H =
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122 Figure 6.8: The real (left) and
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124 E(q) = −M 2 ( 2J2 +2J6 +cos(
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126 For a 2D hexagonal lattice, the
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128 Bibliography [12] P. Ferriani,
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130 Bibliography [39] A. Dallmeyer,
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132 Bibliography [68] J. Perdew and
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134 Bibliography [101] L. Nordströ
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136 Bibliography [130] O. Le Bacq,
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138 Bibliography [160] P. M. Marcus
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140 Bibliography [190] R. Germar, W
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Acknowledgement I don’t know how
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Schriften des Forschungszentrums J
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